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The baryon-antibaryon asymmetry (excess of matter over antimatter in our Universe), indicated by observational data from the Cosmic Microwave Background anisotropies, predictions of primordial Nucleosynthesis, and the absence of intense radiation from matter-antimatter annihilation, constitutes an unsolved puzzle in cosmology. Two mechanisms for baryon asymmetry have been proposed as extensions of the Standard Model of Particle Physics at high energies. They rely on new couplings involving the baryon number current, one with a scalar field, called Spontaneous Baryogenesis, and the other with space-time curvature, named Gravitational Baryogenesis. These two mechanisms are investigated in the context of many bouncing scenarios, either symmetric or asymmetric around the bounce. It is shown that the constraints on the free parameters of these scenarios, imposed to yield the observed baryon-to-entropy ratio, are mild, already containing the values compatible with other observational constraints coming from the features of the power spectra of cosmological perturbations. Hence, realistic bouncing models can yield the observed baryon-antibaryon asymmetry if one of the two mechanisms proposed takes place in nature.